Inventory is the blood-line of supply chains. Yet, most challenges to executing a profitable operations comes from the inability to optimize inventories as they start to propagate across their supply chain.

Buyback contract is a supply chain contract in which a retailer is allowed to return unsold “inventory” up to a specified amount at an agreed upon price to the supplier. This lowers the loss to the retailer and makes it optimal for the retailer to order more quantity resulting in higher product availability, thereby increasing profits for both retailer and supplier.

Buyback contracts are very common in the publishing industry wherein publishers accept unsold books from retailers. To minimize the cost associated with return, retailers do not have to return the book but only the cover. This provides publishers with the proof that book did not sell while reducing the cost of returns. Buyback are common in video-cassette, newspaper and apparel industries also.

Suppose the manufacturer has a production cost vand charges the retailer a price c.Manufacturer buys back at a price b and can sell the returned quantity at a salvage price Sm. Retailer sells each unit at a price p. LetObe the optimal order quantity ordered by the retailer and actual demand is D.

Suppose a manufacturer sells a product to the retailer and the demand for this product is distributed as follows:

Quantity

Probability

100

0.15

110

0.22

120

0.30

130

0.20

140

0.90

150

0.04

Assume that v = 3300, c = 4000, p = 4500 and Sm=2600

Without Buyback Contract:

Under this scenario, a stochastic constrained optimization model that maximizes the retailer’s profit yields the following:

Optimal order size

110

Manufacturer's Profit

77000

Retailer's Profit

522900

Supply Chain Profit

129900

With Buyback Contract:

Both the manufacturer and retailer will enter into a buyback contract only if their profits after the contract are more than their respective profits without buyback contract. To increase their profits, they will now decide optimal order size (O), buyback price (b) and the price (c) such that it will earn maximum profit for both the parties which will ultimately lead to maximization of supply chain profit.

Under this scenario, a stochastic constrained optimization model that maximizes the supply chain profit (Not Retailer’s or Manufacturer’s profit separately) yields the following:

Cost for retailer

3969

Buy back price

3101

Order size

120

Manufacturer's Profit

77675

Retailer's Profit

56445

Supply Chain Profit

134120

We can now easily compare the retailer’s profit, manufacturer’s profit and supply chain profit with those obtained without buyback contract: